Question

quick refresher on eigenvector question.

Answer 1

I have the matrix \[\left[\begin{matrix} 1 & 2 & -1 \\ 0 & 3 & -2 \\ 0 & 2 & -2\end{matrix}\right]\]

Answer 2

and I'm having a bit of trouble when finding the eigenvector associated with eigenvalue \(\lambda=1\)

Answer 3

looking at the bottom two rows I can see that \(x_2=x_3=0\), but I don't understand why the x_1 is arbitrary. Like why is \[(x_1,x_2,x_3)=(1,0,0)\]an eigenvector, how does that not violate the top line?

Answer 4

I can't believe I still mess up finding eigenvectors...

Answer 5

oh nevermind. stupid mistake.